On the use of a discrepancy decomposition model for calibration experiments

Computer simulation models are widely used to study complex physical systems. A related topic is the calibration problem, which aims at learning about the values of parameters in the model based on observations. In most real applications, the parameters have specific physical meanings, and we call them physical parameters. To understand the true underlying physical system, we need to effectively estimate such parameters. However, existing calibration methods have limitations in addressing this issue due to model identifiability. This paper proposes a method based on the discrepancy decomposition model to describe the discrepancy between the physical system and the computer model. The proposed model possesses a clear interpretation, and more importantly, it is identifiable under mild conditions. Under this model, we present estimators of the physical parameters and the discrepancy functions, and then establish their asymptotic properties. Numerical examples show that the proposed method is capable of accurately estimating the physical parameters and quite robust to model assumptions.